What is the Sortino Ratio? Downside Risk Definition & Examples

What is the Sortino Ratio?

The Sortino ratio measures how much return you're getting for the downside risk you're taking, and ignoring upside volatility entirely. That makes it especially useful for assets like Bitcoin that can swing wildly to the upside.

The Sortino ratio is the Sharpe ratio's more opinionated sibling.

Sharpe treats all volatility as “bad”, which doesn’t make much sense if you’re an investor who likes upside surprises. Sortino keeps the same basic idea — return per unit of risk — but it only counts downside volatility as risk.

Sortino Ratio calculator

What is a good Sortino ratio?

While a “good” Sortino ratio depends on the asset class and how you compute it, a practical rule of thumb is:

Benchmarks: crypto vs. traditional assets

Because crypto is so volatile, “good” can look different than it does for the S&P 500:

• Traditional equities: a Sortino ratio above 2.0 is often considered elite.
• Bitcoin / crypto: strong strategies can print Sortino ratios above 3.0 (or even 4.0+) because Sortino ignores upside volatility that would otherwise penalize a Sharpe ratio.

For a concrete example, see our Bitcoin vs Gold (2023) analysis, where Bitcoin delivered an astonishing 3.92 Sortino ratio.

Sortino ratio formula (explained)

$$\text{Sortino} = \frac{E[r] - r_f}{\sigma_{\text{down}}}$$

Where $r$ is the return series (we use daily simple returns from close-to-close), $E[r]$ is the average daily return annualized (not CAGR), $r_f$ is the risk‑free rate, and $\sigma_{\text{down}}$ is downside deviation.

What “downside deviation” means (in human terms)

Downside deviation measures the “bad part” of volatility: how big (and how often) returns fall below a chosen target return. The first step is picking that target (sometimes called MAR: minimum acceptable return). Then you look at the shortfall below that target.

At Gale Finance, the target return is the daily risk‑free rate implied by the annual risk‑free rate:

$$r_f^{\text{daily}} = \frac{r_f}{N}$$

Where $N$ is the annualization factor (typically 365 for crypto/stablecoins and ~252 for trading‑day assets).

So the downside set is "all days where $r_t < r_f^{\text{daily}}$".

How we calculate Sortino at Gale Finance

Most of the methodology mirrors Sharpe:

1. Returns: daily simple returns from close‑to‑close:

$$r_t = \frac{P_t}{P_{t-1}} - 1$$

We don’t forward‑fill missing dates. If an ETF doesn’t trade on a holiday, we don’t invent a “flat” return for that day.

We annualize expected return using the arithmetic mean of daily returns:

$$E[r_{annual}] = \bar{r}_t \times N$$

2. Annualization uses the asset’s calendar: we use 365 for crypto/stablecoins (weekends matter) and ~252 for trading‑day assets (or infer the effective frequency when needed).

3. Risk‑free rate: we use the average 3‑month Treasury rate over the analysis window (FRED series DGS3MO). If we can’t fetch it, we fall back to a configured default.

4. Target return (MAR): some Sortino definitions use 0% as the target return. We use the risk‑free rate instead, which matches the “excess return” idea and keeps Sharpe and Sortino comparable.

5. Downside deviation (LPM2 / semi‑deviation): we use the canonical “lower partial moment of order 2” definition. Days above the target contribute 0; days below contribute their squared shortfall. Then we annualize.

$$\sigma_{\text{down,annual}} = \sqrt{\frac{1}{T}\sum_{t=1}^{T} \min\left(0,\; r_t - \text{MAR}\right)^2}\;\times\sqrt{N}$$

The important detail: the average is taken over all $T$ daily observations (not just downside days). That’s what makes it capture both frequency and magnitude of shortfalls.

If you set $\text{MAR} = r_f/N$, this is the “risk‑free target” version. If you set $\text{MAR} = 0$, it’s the “0% target” version you’ll see in some libraries.

How to read it (and one edge case)

Sortino answers: “how much return did I get for the downside volatility I had to sit through?”

That’s especially useful for assets that can jump around on the upside (crypto is the obvious example). A huge up day can inflate total volatility and make Sharpe look worse, even though nobody is complaining about a big gain. Sortino doesn’t punish that.

One edge case: in a strong bull period, an asset might have zero days below the target return. In that case, downside deviation is 0 and Sortino becomes undefined / not informative. On Gale Finance we show Sortino as N/A for that window and include a short note about sample size.

Even when there are some downside days, a one‑year window can be thin. That’s why compare pages surface a “limited sample” note when there are fewer than 20 downside days in the window (a heuristic, not a statistical test).

If you want a broader picture of “what the ugly days look like”, pair Sortino with tail metrics like VaR / Expected Shortfall and downside co-moves.